Supplement: Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish

Patrycja Strycharczuk, Małgorzata Ćavar, Stefano Coretta

1 Overview

This supplementary document complements the paper Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish.

The following sections illustrate:

The articulatory data normalisation procedure.
Descriptive plots of the raw data.
Code and plots of the linear regression models.
Summaries of the models in 3.
Extra analyses of F0 and F3.

Only relevant R code is shown in this document. The full code can be inspected on the OSF repository at https://osf.io/hy7nt/?view_only=d06775a2cb1d4786a0442b0f15d73296, in the file code/analysis.Rmd.

2 Normalisation procedure

This is Figure 1 from the paper, which illustrates the normalisation procedure. See paper for details.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

3 Descriptive statistics plots

3.1 Articulatory undershoot

Tongue contours from ultrasound tongue imaging of speaker PL01. Tongue tip on the right.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

3.2 Duration

Figure 2 from the paper with boxplots and means of vowel duration depending on speech rate and stress.

3.3 Vowel space

3.3.1 Acoustic vowel space

3.3.2 Articulatory vowel space

3.3.3 Save

4 Inferential statistics

4.1 VIF (multicollinearity)

VIF values below 3 indicate absence of multicollinearity (Zuur, Ieno, and Elphick 2010). For all predictors, VIF < 3.

##   Variables      VIF
## 1  duration 2.169934
## 2      f1.z 1.379401
## 3      f2.z 1.208097
## 4      f0.z 1.122029
## 5      rate 1.639475
## 6    stress 1.451903

4.2 Duration

## NOTE: rate:stress is not a high-order term in the model

## refitting model(s) with ML (instead of REML)

## Data: midpoint_rotated
## Models:
## dur.lmer3: duration.log ~ (rate + stress | speaker) + (1 | frame) + rate * 
## dur.lmer3:     V1 + stress
## dur.lmer2: duration.log ~ (rate + stress | speaker) + (1 | frame) + rate * 
## dur.lmer2:     (V1 + stress)
## dur.lmer.full: duration.log ~ (rate + stress | speaker) + (1 | frame) + rate * 
## dur.lmer.full:     V1 * stress
##               npar     AIC     BIC logLik deviance  Chisq Df Pr(>Chisq)    
## dur.lmer3       31 -291.76 -128.32 176.88  -353.76                         
## dur.lmer2       33 -341.16 -167.17 203.58  -407.16 53.398  2  2.539e-12 ***
## dur.lmer.full   48 -375.61 -122.53 235.81  -471.61 64.450 15  4.265e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4.3 F1

## refitting model(s) with ML (instead of REML)

## Data: midpoint_rotated
## Models:
## f1.lmer.7: f1.z ~ (1 + stress | speaker) + (1 | frame) + duration
## f1.lmer.6: f1.z ~ (1 + stress | speaker) + (1 | frame) + V1
## f1.lmer.5: f1.z ~ (1 + stress | speaker) + (1 | frame) + V1 + duration
## f1.lmer.4: f1.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration
## f1.lmer.3: f1.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration + 
## f1.lmer.3:     stress
## f1.lmer.2: f1.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration + 
## f1.lmer.2:     V1 * stress
## f1.lmer.full: f1.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration * 
## f1.lmer.full:     stress
##              npar    AIC    BIC   logLik deviance   Chisq Df Pr(>Chisq)    
## f1.lmer.7       7 2444.9 2481.8 -1215.47   2430.9                          
## f1.lmer.6      11 2055.4 2113.3 -1016.68   2033.4 397.588  4  < 2.2e-16 ***
## f1.lmer.5      12 1964.6 2027.9  -970.30   1940.6  92.767  1  < 2.2e-16 ***
## f1.lmer.4      17 1693.0 1782.7  -829.52   1659.0 281.553  5  < 2.2e-16 ***
## f1.lmer.3      18 1683.7 1778.6  -823.87   1647.7  11.305  1  0.0007730 ***
## f1.lmer.2      23 1656.5 1777.8  -805.24   1610.5  37.245  5  5.349e-07 ***
## f1.lmer.full   29 1645.9 1798.8  -793.93   1587.9  22.620  6  0.0009342 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4.4 F2

## refitting model(s) with ML (instead of REML)

## Data: midpoint_rotated
## Models:
## f2.lmer.7: f2.z ~ (1 + stress | speaker) + (1 | frame) + duration
## f2.lmer.6: f2.z ~ (1 + stress | speaker) + (1 | frame) + V1
## f2.lmer.5: f2.z ~ (1 + stress | speaker) + (1 | frame) + V1 + duration
## f2.lmer.4: f2.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration
## f2.lmer.3: f2.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration + 
## f2.lmer.3:     stress
## f2.lmer.2: f2.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration + 
## f2.lmer.2:     V1 * stress
## f2.lmer.full: f2.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration * 
## f2.lmer.full:     stress
##              npar     AIC     BIC  logLik deviance    Chisq Df Pr(>Chisq)    
## f2.lmer.7       7 1093.20 1130.11 -539.60  1079.20                           
## f2.lmer.6      11  863.11  921.11 -420.55   841.11 238.0945  4  < 2.2e-16 ***
## f2.lmer.5      12  864.44  927.71 -420.22   840.44   0.6667  1     0.4142    
## f2.lmer.4      17  690.02  779.65 -328.01   656.02 184.4255  5  < 2.2e-16 ***
## f2.lmer.3      18  689.78  784.68 -326.89   653.78   2.2395  1     0.1345    
## f2.lmer.2      23  664.61  785.88 -309.31   618.61  35.1637  5  1.396e-06 ***
## f2.lmer.full   29  673.24  826.14 -307.62   615.24   3.3769  6     0.7603    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4.5 Z1

## refitting model(s) with ML (instead of REML)

## Data: midpoint_rotated
## Models:
## z1.lmer.7: z1 ~ (1 + stress | speaker) + (1 | frame) + duration
## z1.lmer.6: z1 ~ (1 + stress | speaker) + (1 | frame) + V1
## z1.lmer.5: z1 ~ (1 + stress | speaker) + (1 | frame) + V1 + duration
## z1.lmer.4: z1 ~ (1 + stress | speaker) + (1 | frame) + V1 * duration
## z1.lmer.3: z1 ~ (1 + stress | speaker) + (1 | frame) + V1 * duration + stress
## z1.lmer.2: z1 ~ (1 + stress | speaker) + (1 | frame) + V1 * duration + V1 * 
## z1.lmer.2:     stress
## z1.lmer.full: z1 ~ (1 + stress | speaker) + (1 | frame) + V1 * duration * stress
##              npar    AIC    BIC  logLik deviance    Chisq Df Pr(>Chisq)    
## z1.lmer.7       7 1235.4 1272.3 -610.70   1221.4                           
## z1.lmer.6      11 1306.0 1364.0 -642.03   1284.0   0.0000  4     1.0000    
## z1.lmer.5      12 1214.2 1277.4 -595.07   1190.2  93.9022  1     <2e-16 ***
## z1.lmer.4      17 1073.8 1163.5 -519.92   1039.8 150.3004  5     <2e-16 ***
## z1.lmer.3      18 1074.4 1169.3 -519.21   1038.4   1.4195  1     0.2335    
## z1.lmer.2      23 1076.5 1197.7 -515.23   1030.5   7.9689  5     0.1580    
## z1.lmer.full   29 1087.6 1240.5 -514.82   1029.6   0.8246  6     0.9914    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4.6 Z2

## Warning: Model failed to converge with 1 negative eigenvalue: -5.0e+02

## Warning: Model failed to converge with 1 negative eigenvalue: -2.1e-01

4.7 Composite plot

5 Model summaries

5.1 Duration

	duration.log
Predictors	Estimates	CI	p
(Intercept)	3.7705	3.6315 – 3.9096	<0.001
rate [normal]	0.1947	0.0877 – 0.3017	0.00036
rate [slow]	0.4496	0.3067 – 0.5924	<0.001
V11	0.1436	0.0201 – 0.2671	0.02269
V12	-0.0082	-0.1557 – 0.1392	0.91282
V13	0.0034	-0.1641 – 0.1709	0.96803
V14	0.0035	-0.1199 – 0.1270	0.95508
V15	-0.2249	-0.3924 – -0.0575	0.00848
stress [stressed]	0.2263	0.1768 – 0.2757	<0.001
rate [normal] * V11	-0.0110	-0.0906 – 0.0686	0.78591
rate [slow] * V11	-0.0450	-0.1246 – 0.0346	0.26793
rate [normal] * V12	-0.0113	-0.0909 – 0.0683	0.78040
rate [slow] * V12	0.0020	-0.0776 – 0.0816	0.96022
rate [normal] * V13	0.0542	-0.0254 – 0.1338	0.18232
rate [slow] * V13	-0.0227	-0.1023 – 0.0569	0.57624
rate [normal] * V14	-0.0051	-0.0847 – 0.0745	0.90081
rate [slow] * V14	0.0217	-0.0579 – 0.1013	0.59332
rate [normal] * V15	-0.0414	-0.1211 – 0.0382	0.30752
rate [slow] * V15	0.0052	-0.0744 – 0.0848	0.89893
rate [normal] * stress [stressed]	0.1479	0.0975 – 0.1982	<0.001
rate [slow] * stress [stressed]	0.1799	0.1296 – 0.2303	<0.001
V11 * stress [stressed]	0.1206	0.0410 – 0.2002	0.00298
V12 * stress [stressed]	-0.0503	-0.1299 – 0.0293	0.21548
V13 * stress [stressed]	-0.0750	-0.1546 – 0.0047	0.06498
V14 * stress [stressed]	0.0292	-0.0504 – 0.1088	0.47278
V15 * stress [stressed]	-0.0082	-0.0878 – 0.0714	0.84070
(rate [normal] * V11) * stress [stressed]	-0.0257	-0.1383 – 0.0869	0.65480
(rate [slow] * V11) * stress [stressed]	-0.0559	-0.1684 – 0.0567	0.33085
(rate [normal] * V12) * stress [stressed]	-0.0420	-0.1545 – 0.0706	0.46501
(rate [slow] * V12) * stress [stressed]	-0.0430	-0.1555 – 0.0696	0.45454
(rate [normal] * V13) * stress [stressed]	-0.0722	-0.1848 – 0.0403	0.20856
(rate [slow] * V13) * stress [stressed]	-0.0783	-0.1909 – 0.0343	0.17273
(rate [normal] * V14) * stress [stressed]	0.0017	-0.1109 – 0.1142	0.97691
(rate [slow] * V14) * stress [stressed]	0.0339	-0.0787 – 0.1465	0.55538
(rate [normal] * V15) * stress [stressed]	0.1177	0.0051 – 0.2303	0.04043
(rate [slow] * V15) * stress [stressed]	0.1148	0.0022 – 0.2274	0.04562
Random Effects
σ²	0.0396
τ₀₀ _frame	0.0154
τ₀₀ _speaker	0.0351
τ₁₁ _{speaker.ratenormal}	0.0265
τ₁₁ _{speaker.rateslow}	0.0498
τ₁₁ _{speaker.stressstressed}	0.0031
ρ₀₁ _{speaker.ratenormal}	-0.8117
ρ₀₁ _{speaker.rateslow}	-0.7847
ρ₀₁ _{speaker.stressstressed}	-0.4845
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.706 / NA

5.2 F1

	f1.z
Predictors	Estimates	CI	p
(Intercept)	-0.5940	-0.7829 – -0.4052	<0.001
V11	0.3813	0.0395 – 0.7230	0.02879
V12	0.0844	-0.2916 – 0.4603	0.65998
V13	-0.2855	-0.6862 – 0.1152	0.16256
V14	0.3131	-0.0176 – 0.6437	0.06351
V15	-0.4903	-0.9025 – -0.0780	0.01976
duration	0.0073	0.0054 – 0.0091	<0.001
stress [stressed]	0.3986	0.2378 – 0.5594	<0.001
V11 * duration	0.0176	0.0136 – 0.0216	<0.001
V12 * duration	-0.0008	-0.0050 – 0.0034	0.70990
V13 * duration	-0.0095	-0.0131 – -0.0058	<0.001
V14 * duration	-0.0028	-0.0069 – 0.0013	0.18000
V15 * duration	0.0018	-0.0032 – 0.0069	0.47562
V11 * stress [stressed]	0.4096	0.0591 – 0.7601	0.02201
V12 * stress [stressed]	-0.2227	-0.5369 – 0.0915	0.16480
V13 * stress [stressed]	-0.2530	-0.5546 – 0.0487	0.10026
V14 * stress [stressed]	0.1610	-0.1479 – 0.4699	0.30707
V15 * stress [stressed]	0.1846	-0.1275 – 0.4967	0.24627
duration * stress [stressed]	-0.0031	-0.0053 – -0.0009	0.00503
(V11 * duration) * stress [stressed]	-0.0054	-0.0101 – -0.0007	0.02419
(V12 * duration) * stress [stressed]	0.0068	0.0018 – 0.0117	0.00715
(V13 * duration) * stress [stressed]	0.0012	-0.0033 – 0.0057	0.60775
(V14 * duration) * stress [stressed]	0.0009	-0.0037 – 0.0056	0.69239
(V15 * duration) * stress [stressed]	-0.0068	-0.0125 – -0.0011	0.01866
Random Effects
σ²	0.1722
τ₀₀ _frame	0.0694
τ₀₀ _speaker	0.0019
τ₁₁ _{speaker.stressstressed}	0.0138
ρ₀₁ _speaker	-1.0000
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.837 / NA

5.3 F2

	f2.z
Predictors	Estimates	CI	p
(Intercept)	-0.0561	-0.2399 – 0.1277	0.54996
V11	-0.3844	-0.6940 – -0.0747	0.01497
V12	0.2754	-0.0833 – 0.6341	0.13241
V13	1.1731	0.7746 – 1.5716	<0.001
V14	-0.5199	-0.8234 – -0.2164	0.00079
V15	-0.6727	-1.0771 – -0.2683	0.00111
duration	0.0007	-0.0006 – 0.0020	0.28282
stress [stressed]	0.0500	-0.0510 – 0.1509	0.33200
V11 * duration	0.0012	-0.0017 – 0.0040	0.42632
V12 * duration	0.0028	-0.0002 – 0.0058	0.06680
V13 * duration	0.0060	0.0034 – 0.0086	0.00001
V14 * duration	-0.0062	-0.0091 – -0.0033	0.00003
V15 * duration	-0.0058	-0.0094 – -0.0022	0.00158
V11 * stress [stressed]	0.0382	-0.2118 – 0.2882	0.76481
V12 * stress [stressed]	-0.0225	-0.2460 – 0.2009	0.84330
V13 * stress [stressed]	0.2911	0.0761 – 0.5061	0.00797
V14 * stress [stressed]	-0.1243	-0.3448 – 0.0962	0.26927
V15 * stress [stressed]	-0.2552	-0.4777 – -0.0328	0.02451
duration * stress [stressed]	-0.0004	-0.0019 – 0.0011	0.59982
(V11 * duration) * stress [stressed]	-0.0008	-0.0042 – 0.0025	0.62985
(V12 * duration) * stress [stressed]	0.0003	-0.0032 – 0.0038	0.85782
(V13 * duration) * stress [stressed]	-0.0023	-0.0055 – 0.0009	0.15485
(V14 * duration) * stress [stressed]	0.0015	-0.0018 – 0.0048	0.38169
(V15 * duration) * stress [stressed]	0.0012	-0.0029 – 0.0052	0.56628
Random Effects
σ²	0.0879
τ₀₀ _frame	0.0829
τ₀₀ _speaker	0.0000
τ₁₁ _{speaker.stressstressed}	0.0000
ρ₀₁ _speaker
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.908 / NA

5.4 Z1

	z1
Predictors	Estimates	CI	p
(Intercept)	-0.2709	-0.4129 – -0.1289	0.00018
V11	0.1673	-0.0947 – 0.4294	0.21071
V12	-0.1629	-0.4441 – 0.1183	0.25625
V13	-0.5549	-0.8481 – -0.2616	0.00021
V14	0.2548	0.0028 – 0.5067	0.04750
V15	0.1165	-0.1877 – 0.4207	0.45295
duration	0.0043	0.0027 – 0.0058	<0.001
stress [stressed]	-0.0168	-0.1472 – 0.1136	0.80074
V11 * duration	0.0072	0.0038 – 0.0105	0.00002
V12 * duration	-0.0003	-0.0038 – 0.0031	0.85866
V13 * duration	-0.0052	-0.0082 – -0.0022	0.00074
V14 * duration	0.0053	0.0019 – 0.0086	0.00233
V15 * duration	-0.0023	-0.0065 – 0.0019	0.27713
V11 * stress [stressed]	-0.0575	-0.3471 – 0.2320	0.69692
V12 * stress [stressed]	0.0712	-0.1883 – 0.3307	0.59073
V13 * stress [stressed]	-0.0877	-0.3367 – 0.1614	0.49029
V14 * stress [stressed]	0.0318	-0.2233 – 0.2870	0.80673
V15 * stress [stressed]	0.0441	-0.2138 – 0.3021	0.73727
duration * stress [stressed]	-0.0005	-0.0023 – 0.0014	0.61937
(V11 * duration) * stress [stressed]	-0.0007	-0.0046 – 0.0032	0.72195
(V12 * duration) * stress [stressed]	0.0001	-0.0040 – 0.0042	0.95233
(V13 * duration) * stress [stressed]	0.0012	-0.0026 – 0.0049	0.54405
(V14 * duration) * stress [stressed]	0.0003	-0.0036 – 0.0041	0.89076
(V15 * duration) * stress [stressed]	-0.0013	-0.0060 – 0.0034	0.59122
Random Effects
σ²	0.1174
τ₀₀ _frame	0.0327
τ₀₀ _speaker	0.0026
τ₁₁ _{speaker.stressstressed}	0.0072
ρ₀₁ _speaker	-1.0000
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.734 / NA

5.5 Z2

	z2
Predictors	Estimates	CI	p
(Intercept)	0.1281	-0.1131 – 0.3692	0.29785
V11	-0.2655	-0.6556 – 0.1246	0.18225
V12	0.3258	-0.1381 – 0.7898	0.16868
V13	1.0904	0.5657 – 1.6151	0.00005
V14	-0.5343	-0.9192 – -0.1493	0.00653
V15	-0.5867	-1.1162 – -0.0573	0.02985
duration	-0.0020	-0.0033 – -0.0006	0.00405
stress [stressed]	-0.0448	-0.1505 – 0.0609	0.40641
V11 * duration	-0.0007	-0.0036 – 0.0023	0.64961
V12 * duration	0.0008	-0.0023 – 0.0039	0.60673
V13 * duration	0.0042	0.0015 – 0.0069	0.00218
V14 * duration	-0.0044	-0.0074 – -0.0013	0.00456
V15 * duration	-0.0050	-0.0087 – -0.0013	0.00748
V11 * stress [stressed]	0.0914	-0.1664 – 0.3492	0.48723
V12 * stress [stressed]	-0.0858	-0.3164 – 0.1448	0.46602
V13 * stress [stressed]	0.0211	-0.2007 – 0.2429	0.85202
V14 * stress [stressed]	0.0862	-0.1411 – 0.3135	0.45734
V15 * stress [stressed]	-0.1903	-0.4197 – 0.0390	0.10387
duration * stress [stressed]	0.0009	-0.0007 – 0.0025	0.26995
(V11 * duration) * stress [stressed]	-0.0017	-0.0052 – 0.0017	0.32639
(V12 * duration) * stress [stressed]	0.0005	-0.0031 – 0.0041	0.77948
(V13 * duration) * stress [stressed]	0.0007	-0.0026 – 0.0041	0.65806
(V14 * duration) * stress [stressed]	-0.0018	-0.0052 – 0.0017	0.31172
(V15 * duration) * stress [stressed]	0.0034	-0.0008 – 0.0075	0.11437
Random Effects
σ²	0.0934
τ₀₀ _frame	0.1539
τ₀₀ _speaker	0.0000
τ₁₁ _{speaker.stressstressed}	0.0008
ρ₀₁ _speaker
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.874 / NA

6 Further exploratory analyses

6.1 F0

## Warning: Removed 4 rows containing missing values (geom_point).

## Warning: Removed 4 rows containing missing values (geom_point).

	f0.z
Predictors	Estimates	CI	p
(Intercept)	-0.93	-1.30 – -0.55	<0.001
V11	0.30	-0.18 – 0.77	0.217
V12	-0.21	-0.67 – 0.24	0.361
V13	0.07	-0.37 – 0.51	0.747
V14	-0.04	-0.48 – 0.40	0.853
V15	0.13	-0.35 – 0.60	0.595
duration	0.01	0.01 – 0.02	<0.001
stress [stressed]	0.81	0.11 – 1.51	0.023
V11 * duration	-0.01	-0.02 – -0.00	0.005
V12 * duration	0.00	-0.01 – 0.01	0.802
V13 * duration	-0.00	-0.01 – 0.00	0.591
V14 * duration	-0.00	-0.01 – 0.01	0.639
V15 * duration	0.01	0.00 – 0.02	0.013
V11 * stress [stressed]	-0.28	-0.91 – 0.35	0.379
V12 * stress [stressed]	0.42	-0.14 – 0.98	0.142
V13 * stress [stressed]	-0.28	-0.81 – 0.26	0.311
V14 * stress [stressed]	0.01	-0.54 – 0.56	0.966
V15 * stress [stressed]	0.31	-0.24 – 0.87	0.268
duration * stress [stressed]	-0.01	-0.01 – -0.00	<0.001
(V11 * duration) * stress [stressed]	0.01	-0.00 – 0.01	0.218
(V12 * duration) * stress [stressed]	-0.01	-0.02 – 0.00	0.091
(V13 * duration) * stress [stressed]	0.01	-0.00 – 0.01	0.190
(V14 * duration) * stress [stressed]	0.00	-0.01 – 0.01	0.938
(V15 * duration) * stress [stressed]	-0.01	-0.02 – 0.00	0.194
Random Effects
σ²	0.54
τ₀₀ _frame	0.03
τ₀₀ _speaker	0.24
τ₁₁ _{speaker.stressstressed}	1.11
ρ₀₁ _speaker	-1.00
N _speaker	10
N _frame	12
Observations	1436
Marginal R² / Conditional R²	0.257 / NA

6.2 F3

## `geom_smooth()` using formula 'y ~ x'

7 Session info

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.3 (2020-10-10)
##  os       macOS Big Sur 10.16         
##  system   x86_64, darwin17.0          
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Europe/Berlin               
##  date     2021-04-02                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  ! package      * version    date       lib
##  P abind          1.4-5      2016-07-21 [?]
##  P assertthat     0.2.1      2019-03-21 [?]
##  P backports      1.2.1      2020-12-09 [?]
##  P bayestestR     0.8.2      2021-01-26 [?]
##  P bookdown       0.21       2020-10-13 [?]
##  P boot           1.3-27     2021-02-12 [?]
##  P broom          0.7.5      2021-02-19 [?]
##  P cachem         1.0.4      2021-02-13 [?]
##  P callr          3.5.1      2020-10-13 [?]
##  P car            3.0-10     2020-09-29 [?]
##  P carData      * 3.0-4      2020-05-22 [?]
##  P cellranger     1.1.0      2016-07-27 [?]
##  P cli            2.3.1      2021-02-23 [?]
##  P codetools      0.2-18     2020-11-04 [4]
##  P colorspace     2.0-0      2020-11-11 [?]
##  P crayon         1.4.1      2021-02-08 [?]
##  P curl           4.3        2019-12-02 [?]
##  P data.table     1.14.0     2021-02-21 [?]
##  P DBI            1.1.1      2021-01-15 [?]
##  P dbplyr         2.1.0      2021-02-03 [?]
##  P desc           1.3.0      2021-03-05 [?]
##  P devtools       2.3.2      2020-09-18 [?]
##  P digest         0.6.27     2020-10-24 [?]
##  P dplyr        * 1.0.5      2021-03-05 [?]
##  P effects      * 4.2-0      2020-08-11 [?]
##  P effectsize     0.4.4      2021-03-14 [?]
##  P ellipsis       0.3.1      2020-05-15 [?]
##  P emmeans        1.5.5-1    2021-03-21 [?]
##  P estimability   1.3        2018-02-11 [?]
##  P evaluate       0.14       2019-05-28 [?]
##  P fansi          0.4.2      2021-01-15 [?]
##  P farver         2.1.0      2021-02-28 [?]
##  P fastmap        1.1.0      2021-01-25 [?]
##  P forcats      * 0.5.1      2021-01-27 [?]
##  P foreign        0.8-81     2020-12-22 [?]
##  P fs             1.5.0      2020-07-31 [?]
##  P generics       0.1.0      2020-10-31 [?]
##  P ggeffects      1.0.2      2021-03-17 [?]
##  P ggplot2      * 3.3.3      2020-12-30 [?]
##  P ggpubr       * 0.4.0      2020-06-27 [?]
##  P ggrepel      * 0.9.1      2021-01-15 [?]
##  P ggsignif       0.6.1      2021-02-23 [?]
##  P glue           1.4.2      2020-08-27 [?]
##  P gtable         0.3.0      2019-03-25 [?]
##  P haven          2.3.1      2020-06-01 [?]
##  P here           1.0.1      2020-12-13 [?]
##  P highr          0.8        2019-03-20 [?]
##  P hms            1.0.0      2021-01-13 [?]
##  P htmltools      0.5.1.1    2021-01-22 [?]
##  P httr           1.4.2      2020-07-20 [?]
##  P insight        0.13.1     2021-02-22 [?]
##  P jsonlite       1.7.2      2020-12-09 [?]
##  P knitr          1.31       2021-01-27 [?]
##  P labeling       0.4.2      2020-10-20 [?]
##  P lattice        0.20-41    2020-04-02 [4]
##  P lifecycle      1.0.0      2021-02-15 [?]
##  P lme4         * 1.1-26     2020-12-01 [?]
##  P lmerTest     * 3.1-3      2020-10-23 [?]
##  P lubridate      1.7.10     2021-02-26 [?]
##  P magrittr       2.0.1      2020-11-17 [?]
##  P MASS           7.3-53.1   2021-02-12 [?]
##  P Matrix       * 1.3-2      2021-01-06 [?]
##  P memoise        2.0.0      2021-01-26 [?]
##  P mgcv           1.8-34     2021-02-16 [?]
##  P minqa          1.2.4      2014-10-09 [?]
##  P mitools        2.4        2019-04-26 [?]
##  P modelr         0.1.8      2020-05-19 [?]
##  P munsell        0.5.0      2018-06-12 [?]
##  P mvtnorm        1.1-1      2020-06-09 [?]
##  P nlme           3.1-152    2021-02-04 [?]
##  P nloptr         1.2.2.2    2020-07-02 [?]
##  P nnet           7.3-15     2021-01-24 [?]
##  P numDeriv       2016.8-1.1 2019-06-06 [?]
##  P openxlsx       4.2.3      2020-10-27 [?]
##  P optimx       * 2020-4.2   2020-04-08 [?]
##  P parameters     0.12.0     2021-02-21 [?]
##  P patchwork    * 1.1.1      2020-12-17 [?]
##  P performance  * 0.7.0      2021-02-03 [?]
##  P pillar         1.5.1      2021-03-05 [?]
##  P pkgbuild       1.2.0      2020-12-15 [?]
##  P pkgconfig      2.0.3      2019-09-22 [?]
##  P pkgload        1.2.0      2021-02-23 [?]
##  P prettyunits    1.1.1      2020-01-24 [?]
##  P processx       3.5.0      2021-03-23 [?]
##  P ps             1.6.0      2021-02-28 [?]
##  P purrr        * 0.3.4      2020-04-17 [?]
##  P R6             2.5.0      2020-10-28 [?]
##  P raster       * 3.4-5      2020-11-14 [?]
##  P Rcpp           1.0.6      2021-01-15 [?]
##  P readr        * 1.4.0      2020-10-05 [?]
##  P readxl         1.3.1      2019-03-13 [?]
##  P remotes        2.2.0      2020-07-21 [?]
##  P reprex         1.0.0      2021-01-27 [?]
##  P rio            0.5.26     2021-03-01 [?]
##  P rlang          0.4.10     2020-12-30 [?]
##  P rmarkdown      2.7        2021-02-19 [?]
##  P rmdformats     1.0.1      2021-01-13 [?]
##  P rprojroot      2.0.2      2020-11-15 [?]
##  P rstatix        0.7.0      2021-02-13 [?]
##  P rstudioapi     0.13       2020-11-12 [?]
##  P rticulate    * 1.6.0      2021-03-18 [?]
##  P rvest          1.0.0      2021-03-09 [?]
##  P scales         1.1.1      2020-05-11 [?]
##  P sessioninfo    1.1.1      2018-11-05 [?]
##  P sjlabelled     1.1.7      2020-09-24 [?]
##  P sjmisc         2.8.6      2021-01-07 [?]
##  P sjPlot       * 2.8.7      2021-01-10 [?]
##  P sjstats        0.18.1     2021-01-09 [?]
##  P sp           * 1.4-5      2021-01-10 [?]
##  P statmod        1.4.35     2020-10-19 [?]
##  P stringi        1.5.3      2020-09-09 [?]
##  P stringr      * 1.4.0      2019-02-10 [?]
##  P survey         4.0        2020-04-03 [?]
##  P survival       3.2-10     2021-03-16 [?]
##  P testthat       3.0.2      2021-02-14 [?]
##  P tibble       * 3.1.0      2021-02-25 [?]
##  P tidymv         3.2.0      2021-01-05 [?]
##  P tidyr        * 1.1.3      2021-03-03 [?]
##  P tidyselect     1.1.0      2020-05-11 [?]
##  P tidyverse    * 1.3.0      2019-11-21 [?]
##  P usdm         * 1.1-18     2017-06-25 [?]
##  P usethis        2.0.1      2021-02-10 [?]
##  P utf8           1.2.1      2021-03-12 [?]
##  P vctrs          0.3.6      2020-12-17 [?]
##  P withr          2.4.1      2021-01-26 [?]
##  P xfun           0.22       2021-03-11 [?]
##  P xml2           1.3.2      2020-04-23 [?]
##  P xtable         1.8-4      2019-04-21 [?]
##  P yaml           2.2.1      2020-02-01 [?]
##  P zip            2.1.1      2020-08-27 [?]
##  source                                   
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## 
## [1] /Users/ste/repos/polish-reduction/renv/library/R-4.0/x86_64-apple-darwin17.0
## [2] /private/var/folders/yj/b5zvw9lj2zg6tp920wyg14y80000gn/T/RtmpeHTEWO/renv-system-library
## [3] /Library/Frameworks/R.framework/Versions/4.0/Resources/site-library
## [4] /Library/Frameworks/R.framework/Versions/4.0/Resources/library
## 
##  P ── Loaded and on-disk path mismatch.

Zuur, Alain F., Elena N. Ieno, and Chris S. Elphick. 2010. “A Protocol for Data Exploration to Avoid Common Statistical Problems.” Methods in Ecology and Evolution 1 (1): 3–14. https://doi.org/10.1111/j.2041-210X.2009.00001.x.